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    <title>hankelsv</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>hankelsv</b> -  Hankel singular values</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[nk2,W]=hankelsv(sl [,tol])  </tt>
      </dd>
      <dd>
        <tt>[nk2]=hankelsv(sl [,tol])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>sl</b>
        </tt>: <tt>
          <b>syslin</b>
        </tt> list representing the linear system (state-space).</li>
      <li>
        <tt>
          <b>tol</b>
        </tt>: tolerance parameter for detecting imaginary axis modes (default value is <tt>
          <b>1000*%eps</b>
        </tt>).</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    returns <tt>
        <b>nk2</b>
      </tt>, the squared Hankel singular values of <tt>
        <b>sl</b>
      </tt>
    and <tt>
        <b>W = P*Q</b>
      </tt> = controllability gramian times observability
    gramian.</p>
    <p>
      <tt>
        <b>nk2</b>
      </tt> is the vector of eigenvalues of <tt>
        <b>W</b>
      </tt>.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=diag([-1,-2,-3]);
sl=syslin('c',A,rand(3,2),rand(2,3));[nk2,W]=hankelsv(sl)
[Q,M]=pbig(W,nk2(2)-%eps,'c');
slr=projsl(sl,Q,M);hankelsv(slr)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../control/balreal.htm">
        <tt>
          <b>balreal</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../control/equil.htm">
        <tt>
          <b>equil</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../control/equil1.htm">
        <tt>
          <b>equil1</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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